SIAM Journal on Numerical Analysis
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Solving ordinary differential equations I (2nd revised. ed.): nonstiff problems
Uniform Error Analysis for Lagrange--Galerkin Approximations of Convection-Dominated Problems
SIAM Journal on Numerical Analysis
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In this work we continue analyzing mathematically the Monod model for biochemically reacting contaminant transport in the subsurface with regard to higher order regularity of solutions as well as further establishing a higher order approximation scheme in terms of an a priori error analysis relying on the regularity results. Recently, the existence and uniqueness of nonnegative global strong solutions to the Monod model was proved by Merz in [Adv. Math. Sci. (2005), in press]. The approximation scheme, based on higher order finite element methods and backward differentiation formulae, was suggested and analyzed numerically by Bause in [Comput. Visual. Sci 7 (2004) 61; M. Feistauer et al. (Eds.), Numerical Mathematics and Advanced Applications, ENUMATH 2003, Springer, 2004, pp. 112-122]. It was successfully applied to test problems of the literature (cf. [Internat. J. Numer. Methods Fluids 40 (2002) 79; IMA J. Numer. Anal. 22 (2002) 253]) as well as to complex scenarios with an additional calculation of the flow field by solving the parabolic-elliptic degenerate Richards equation; cf. [Comput. Visual. Sci. 7 (2004) 61]. The higher order approach has shown to reduce significantly the amount of inherent numerical diffusion compared to lower order ones. Thereby an artificial transverse mixing of the species leading to a strong overestimation of the biodegradation process and wrong prediction is avoided. To illustrate our approach, in this work the movement and expansion of a BTEX plume is studied for a "real world" field scale site.